If your custards are watery, you may be over-baking them. Once eggs get cooked too long, out comes the water.

Baked custards can be (in order of richness):
Simple cup custards (just milk and whole eggs)
Flan/creme caramel/creme reenverse (milk and whole eggs and sometimes yolks, caramel sauce)
Crema Catalana (Spanish counterpart to creme brûlée, but less rich since it uses milk or a mixture of milk and cream and yolks, flavored with citrus and cinnamon rather than vanilla, caramelized top; some are cooked stovetop instead of baked and contain cornstarch)
Pots de creme (milk and cream plus whole eggs and/or yolks)
Creme brûlée (cream and yolks, caramelized top)

There are also custards made with no milk, like orange flans, but that's a different matter.

The photo there is most likely a pot de creme. And if they're calling it a baked custard, it most likely is pot de creme. They brown naturally as they bake, but not much unless they are caramel pots de creme or use brown sugar. Are you sure what you're getting doesn't have the top caramelized like a creme brûlée?

I honestly don't know. I first ate one at Piccadilly Cafeteria, which is something like maybe S&W Cafeterias? All of these are down South.

I know it's some sort of really basic custard in a little ramekin/custard cup. The ones I made at home was very similar, but not quite as good. I couldn't get mine browned on top like the ones at Piccadilly's.

I don't even know what they call it, tbh....

So I can get a good browned top with brown sugar? I have no idea what they do to them to get them so brown. I always go to Piccadilly on the day they're not serving them, and I'm tired of waiting on them.

I'm saying that brown sugar will produce a darker custard, but the browning that occurs in a basic vanilla custard is minimal. If its really brown, then they probably caramelize the top.

The photo is a pot de creme. Custards made with all whole eggs and milk have a sturdier texture than that (just think flan). Just search for a vanilla pot de creme recipe. Then top with sugar and caramelize with a blowtorch or under a broiler.

When I was little, my grandparents always took us to Piccadilly and my grandmother ALWAYS got that custard (I always got fried fish and three vegetables - fries, mac and cheese, and a roll. In Piccadilly land, those count as vegetables, and in grandparent land, they will let that slide). Also, green jello. Apparently I was kind of a simple kid.

ANYWAY, that exact custard is something I crave all the time...just not enough to go to Piccadilly. I bet we are not the only ones who like it. I'm off to google.

I googled and it's listed as "caramel custard." Caramel custard= flan or creme caramel/reenverse depending what country you favor.
It seems likely since flan is the cheapest to make since it's just milk and eggs, unlike the more expensive custards that use cream and yolks.

Always add a pinch of salt.
The important thing is not to overbake. Like I said, if your custard is watery, it means your eggs have gotten to the stage where they're weeping from curdling.
A water bath is not optional, in spite of what the first recipe says.